I recently had a blitz game which came to a rook + pawn vs. rook endgame. My opponent resigned in the following position:

Black can reach Lucena position here: 74. Kd1 Rc5 75. Rg8+ Kf3 76. Rf8+ Kg2 77. Rg8+ Kf1

and then it’s a known win: 78. Rg7 Rd5+ 79. Kc1 Ke2 80. Re7+ Kf3 81. Rf7+ Ke3 82. Re7+ Kf4 83. Rf7+ Rf5

By the way, Crafty found a neat and faster win – 74. … Rc8!

After I looked at all this stuff I thought that my opponent probably missed a draw earlier.  With a help of online Nalimov tablebases I found the moment where it went wrong for him:

Only rook moves – Rd2, Rd5, Rd6, Rd7, Rd8 lead to a draw. It is actually a second method of defense in Philidor position when white rook can’t get to the third line. It was found by M. Karshtedt, that you still can draw by checking from behind. White king should stay on the short side, to allow, if necessary, checks from the long side.
In my game White lost after 70. Kf2 Rc2+ 71. Ke1 Kg3 72. Rd3+ f3 73. Rd8 f2+.